Annuity Calculator
Last updated: 27 June 2026
Reviewed by Gavin Meiring, Lead research and primary author · Doctoral Candidate (Corporate Governance) · Research and drafting assisted by AI
- The word 'annuity' comes from the Latin 'annua', meaning annual payments — and ancient Rome already had contracts where a citizen paid a lump sum in exchange for lifetime income paid out yearly.
- The tontine, a pooled annuity invented by Italian banker Lorenzo de Tonti in 1653, paid survivors ever-larger shares as members died — and governments used it for centuries to raise money.
- Modern annuity pricing rests on actuarial tables, and the first proper life table was published in 1693 by Edmond Halley — the astronomer of Halley's Comet — using birth and death records from the city of Breslau.
Annuity Calculator
An annuity calculator works out either the regular payment an annuity will provide, or the lump sum needed to fund a series of regular payments, based on the interest rate, payment frequency, and number of periods. It is used by retirees assessing pension annuity quotes, financial planners modelling income streams, and anyone evaluating whether a series of future payments is worth a lump sum today.
How to Use the Annuity Calculator
- Choose whether you want to calculate the payment amount or the present value (lump sum).
- Enter the relevant known values: lump sum or payment amount, annual interest rate, number of years, and payment frequency (monthly, quarterly, or annually).
- Select whether payments occur at the start of each period (annuity due) or the end (ordinary annuity).
- Click calculate to see the result.
The Formula
Present value of an ordinary annuity (payments at end of period):
PV = PMT x (1 - (1 + r)^(-n)) / r
Payment amount given a present value:
PMT = PV x r / (1 - (1 + r)^(-n))
Where PV is the present value (lump sum), PMT is the periodic payment, r is the interest rate per period (annual rate / payment frequency), and n is the total number of payments.
For an annuity due (payments at the start of each period), multiply the result by (1 + r).
Real-World Example
A retiree has a pension pot of £200,000 and receives a quote for a level annuity at 5% per annum, paying monthly for 20 years.
- Monthly rate: 5% / 12 / 100 = 0.004167
- Number of payments: 20 x 12 = 240
PMT = £200,000 x 0.004167 / (1 - (1.004167)^(-240)) PMT = £833.33 / (1 - 0.3697) PMT = £833.33 / 0.6303 PMT = approximately £1,322 per month
Total received over 20 years: £1,322 x 240 = £317,280. The retiree receives £117,280 more than the initial lump sum, reflecting the interest earned on the remaining balance throughout the drawdown period.
Annuities in Retirement Planning
In the UK, defined benefit pensions pay a guaranteed annuity-style income for life. With a defined contribution pension, you can purchase an annuity from an insurance company to convert your pot into a guaranteed income stream. Annuities provide certainty: you cannot outlive a lifetime annuity, and the income is guaranteed regardless of investment market performance. The trade-off is that if you die early, the payments stop (unless you purchased a guarantee period or joint-life option), and a level annuity loses purchasing power over time as inflation erodes its real value. Alternatives to purchasing an annuity include drawdown, which keeps the pot invested and takes withdrawals, offering more flexibility and potential growth but with the risk that the pot could run out. Compare annuity quotes from multiple providers using the open market option before committing.
Frequently Asked Questions
What is the difference between a level annuity and an index-linked annuity? A level annuity pays a fixed amount throughout its term, regardless of inflation. An index-linked annuity increases payments each year in line with an index such as the Retail Prices Index (RPI) or Consumer Prices Index (CPI). Index-linked annuities start at a lower payment than level ones but preserve purchasing power over a long retirement. For a 20- to 30-year retirement, inflation protection is usually worth the lower starting income.
Can I leave an annuity to my beneficiaries? A standard lifetime annuity without added features stops paying on death. You can add a guarantee period (typically 5 to 10 years), which means payments continue for the remaining guarantee period even if you die within it. A joint-life annuity continues paying to a surviving spouse or partner, typically at 50% or 66% of the original amount. Both options reduce the starting income. Capital protection options are also available but tend to offer poor value.
At what age should I buy an annuity? Annuity rates improve with age because the insurance company expects to pay for fewer years. Buying at 75 rather than 65 can produce a payment 50% to 70% higher for the same pot. However, the years between 65 and 75 when you could have been drawing income also matter. Many people use drawdown in early retirement and consider converting part or all of their pot to an annuity at 75 to 80, providing a guaranteed income floor in later years when managing investments becomes more difficult.
How are annuity payments taxed? Annuity income is taxed as regular income in the year it is received. If the annuity is funded from a pension pot, the payments are taxable above the personal allowance in the usual way. If funded from non-pension savings (a purchased life annuity), only the interest element is taxable; the capital element is treated as a return of your own money and is not taxable.
What the same pot pays at other rates and terms
The pot in the example above is £200,000 and the quote is level with monthly payments. Holding the pot fixed and moving the rate and the term gives the following monthly payments.
| Rate | 15 years | 20 years | 25 years | | 4% | £1,479 | £1,212 | £1,056 | | 5% | £1,582 | £1,320 | £1,169 | | 6% | £1,688 | £1,433 | £1,289 |
Two patterns come off that table. A longer term lowers the payment because the same pot spreads across more months. A higher rate raises the payment, which surprises people: at 6% the insurer pays more each month than at 4% over the same term and still exhausts the pot at the end of it, because the remaining balance earns more between payments.
Total income moves the other way. At 5% over 15 years the retiree receives £284,686 in total. Over 25 years at the same rate the total is £350,754, which is £150,754 more than the pot itself. A 25-year term at 6% pays £386,581 in total.
Two details shift the numbers again. Payments at the start of each month, an annuity due, multiply the monthly figure by (1 + r), so £1,319.91 becomes £1,325.41. And a level payment loses ground to inflation: £1,319.91 paid 20 years from now buys about £805 worth of goods at 2.5% inflation a year.
Method note: the worked example above rounds the monthly rate to 0.004167 and the discount factor to 0.3697 before dividing, which returns £1,322. Running the same formula at full precision returns £1,319.91. That gap of about £2 a month comes from the rounding, not from a difference in the formula.
Also try these free tools:
Extended Reference Notes
The notes below cover the broader context that informs how to use the Annuity Calculator well.
Typical Input Ranges
Most real-world uses of the Annuity Calculator fall into a middle band where the result is stable and useful. Very small inputs to the Annuity Calculator often round to zero or near-zero, and very large inputs amplify every rounding error in the calculation. The middle band, where the Annuity Calculator inputs are ordinary sizes, is where the tool is most reliable.
Assumptions Behind the Formula
The Annuity Calculator assumes the inputs stay fixed across the period or scenario being modelled. Rates move, values change, and fees appear, so treat the Annuity Calculator output as a clean reference and layer in the frictions your own situation adds.
Common Edge Cases
Three situations change the Annuity Calculator answer in ways the formula does not surface: boundary values near zero, rounding cascades across many steps, and unit mismatches between fields. When any of these apply, sanity-check the Annuity Calculator result against an independent estimate.
When to Revisit the Calculation
The Annuity Calculator output is only as current as its inputs, so re-run the calculation whenever a key value changes materially. A quarterly re-check of the Annuity Calculator suits personal planning; monthly suits active business or investment decisions.
Relationship to Other Tools
The Annuity Calculator shares inputs and outputs with the other tools in its category. If the same numbers feed several tools, capture them once and run each tool so the comparison stays consistent with the Annuity Calculator.
Practical Checklist Before Relying on the Result
Before acting on the Annuity Calculator output, run a short mental checklist: inputs in the right units, direction of the result matching intuition, and magnitude plausible. Each check takes seconds and catches the most common classes of Annuity Calculator error before they reach a decision.
Putting the Result to Work
A single Annuity Calculator run usually narrows the range of plausible answers rather than settling the question. Compare the Annuity Calculator result against a benchmark or a previous run, and ask what would have to change for the answer to flip a decision.
Sensitivity to Inputs
Some inputs move the Annuity Calculator result more than others; changing each by a small amount shows which ones matter. Spend the effort on the high-impact Annuity Calculator inputs and treat the low-impact ones as approximate.
A Note on Stale Inputs
A calculation is only as fresh as the inputs that feed it, so note the date the Annuity Calculator inputs were last refreshed. A six-month-old Annuity Calculator result can be as wrong as a wrong calculation when the underlying values have moved on.